Summary: POINTWISE CONVERGENCE OF AVERAGES ALONG CUBES
I. ASSANI
Abstract. Let (X, B, µ, T) be a measure preserving system. We prove the pointwise
convergence of the averages
1
N2
N-1
n,m=0
f1(Tn
x)f2(Tm
x)f3(Tn+m
x)
and of similar averages with seven bounded functions.
1. Introduction
In [3], V. Bergelson generalized Khintchine's theorem [6] by proving the L2 convergence
of the averages
1
N2
N-1
n,m=0

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

Collections: Mathematics